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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 64, Issue 3

Issues

The Euler characteristic and valuations on MV-algebras

Daniele Mundici
  • Department of Mathematics and Computer Science “Ulisse Dini”, University of Florence, viale Morgagni 67/A, 50134, Florence, Italy
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/ Andrea Pedrini
Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0226-6

Abstract

Every finitely presented MV-algebra A has a unique idempotent valuation E assigning value 1 to every basic element of A. For each a ∈ A, E(a) turns out to coincide with the Euler characteristic of the open set of maximal ideals m of A such that a/m is nonzero.

MSC: Primary 06D35; Secondary 57Q05, 52B05, 55U10.

Keywords: Euler characteristic; valuation; MV-algebra; basis; rational polyhedron; finite presentation; duality; inclusion-exclusion; additivity; Morse theory; Turing computable valuation

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About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 563–570, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0226-6.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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